An inequality with application to multivariate analysis

Abstract

An inequality for the trace of the product of two symmetric matrices can be used to simplify the proofs of a number of results in multivariate analysis. This is illustrated on two problems: estimating the parametere of a multivariate normal population, and estimating a system of linear functional relationships between the mean vectors of k multivariate normal populations with the same dispersion matrix. A new result is proved for the corresponding structural relationship problem.